Ilya Bryzgalov stopped 33 shots for his fourth victory of the season.
"It was really important to give us our confidence back," said Bryzgalov. "Last game was like a bad dream. We know how we can play and can fight and win the game. It was a really good game. I feel really confident and the guys played well in front of me. This was really important and now the team is back on track again."
The victory was the Ducks' first since defeating San Jose on December 26 and runs Anaheim's NHL-best record to 29-9-6 with 64 points.
"Our message after the game Friday night was that it was unacceptable," said Ducks head coach Randy Carlyle. "The only way we were going to be able to prevent what happened Friday from happening again was to have 20 guys give us their best 60 minutes."
After a scoreless first period, the Ducks struck for three tallies in the second.
Moen opened the scoring at 1:15 of the second period with his sixth goal of the season. Moen fired a wrist shot from the right wing that tipped off the stick of Detroit defenseman Danny Markov and past Dominik Hasek to give the Ducks a 1-0 lead.
The Red Wings countered two minutes and three seconds later on the power play when Mikael Samuelsson grabbed a rebound off the end boards and tucked it inside the post for his 11th goal of the season.
Anaheim capitalized on another deflection at 10:36 of the second when Melin's attempted pass to linemate Andy McDonald was deflected by Red Wings defenseman Brett Lebda and past Hasek. The goal was the first NHL tally for Melin who was called up from Portland on Thursday and was making his NHL debut.
"Teemu got the puck and gave me a real nice pass," said Melin. "I saw Andy go to the net and tried to give it to him, but I hit the defenseman's stick instead. It made me relax a little bit."
Getzlaf gave Anaheim a 3-1 second period lead at 12:39 with a rocket slap shot from the top of the right face off circle.
Tomas Holmstrom cut the Ducks lead to 3-2 with his ninth goal of the season at 2:14 of the third period. The play was reviewed to determine if Holmstrom illegally redirected the puck with his skate.
The Ducks now head back to the road to face Nashville on Tuesday and Dallas on Thursday. Anaheim will return to Honda Center ice Saturday against the Colorado Avalanche at 7:05 p.m.
20:00 - END OF GAME. Shots on goal - ANA 6-27, DET 17-35
19:56 - ANAHEIM GOAL - EMPTY NET - ROB NIEDERMAYER (4).
8:42 - ANA PEN - Scott Niedermayer for interference. Detroit gets their seventh power play. They are 2-for-6 in the game.
2:14 - ANA PEN - Sean O'Donnell for slashing. Detroit goes on their sixth power play - they are 2-for-5 in the game.
2:14 - DETROIT GOAL - POWER PLAY - TOMAS HOLMSTROM (9). Holmstrom redirects a loose puck with his skate and past Ilya Bryzgalov to cut the Anaheim lead to 3-2. The assists go to Henrik Zetterberg and Niklas Lidstrom.
1:31 - ANA PEN - Joe DiPenta for high sticking. Detroit goes on their fifth power play. The Red Wings are 1-for-4 tonight with the man advantage.
0:00 - The third period is under way at Honda Center.
20:00 - END OF 2ND PERIOD. Shots on goal - ANA 9-21, DET 11-18
19:14 - ANA PEN - Tim Brent for slashing. Detroit goes on its fourth power play - they are 1-for-3 today with the man advantage.
12:39 - ANAHEIM GOAL - RYAN GETZLAF (17). Getzlaf beats Dominik Hasek with a rocket slap shot from the top of the right face off circle. Assists on the goal go to Chris Kunitz and Scott Niedermayer.
10:36 - ANAHEIM GOAL - BJORN MELIN (1). Melin attempts a pass through the slot to Andy McDonald that is deflected by Detroit defenseman Brett Lebda and past Dominik Hasek. The lone assist on the goal goes to Teemu Selanne.
3:18 - DETROIT GOAL - POWER PLAY - MIKAEL SAMUELSSON (11). Niklas Kronwall's slap shot from the point goes wide and rebounds off the end boards and behind the net to Samuelsson on the doorstep. Samuelsson tucks the loose puck into the far post with assists going to Kronwall and Robert Lang.
3:07 - ANA PEN - Sean O'Donnell for holding. Detroit goes on its third power play.
1:15 - It was announced in the press box that Detroit defenseman Mathieu Schneider has left the game with a lower body injury and will not return.
1:15 - ANAHEIM GOAL - TRAVIS MOEN (6). Moen unleashes a wrist shot streaking down the right wing that deflects off the stick of defenseman Danny Markov and inside the far post. Assists go to Samuel Pahlsson and Sean O'Donnell.
0:00 - The second period has begun. The Ducks will be shorthanded for 1:05 to start the period.
20:00 - END OF 1ST PERIOD. Shots on goal: ANA 12, DET 7
19:04 - ANA PEN - Rob Niedermayer for holding. Detroit goes on its second power play.
13:44 - DET PEN - Kris Draper for cross checking. Anaheim goes on its second power play of the game.
9:20 - DET PEN - Johan Franzen for hooking. Anaheim goes on its first power play. The Ducks are operating at 22% (3rd NHL) with the man advantage. Detroit is killing at 81% (20th NHL).
1:09 - ANA PEN - Rob Niedermayer for hooking. Detroit goes on its first power play. The Red Wings are operating at 15.1% this season with the man advantage (24th NHL). The Ducks are killing at 85.3% (7th NHL).
0:00 - The first period is under way at Honda Center.
Ducks goaltender JS Giguere was honored by the Ducks and the NHL prior to the opening face off for earning 25 career shutouts. Giguere recently shut out Nashville on December 6 for shut out number 25.
Starting Goaltenders: ANA 30 Ilya Bryzgalov; DET 39 Dominik Hasek
Scratches: ANA 35 G JS Giguere, 16 RW George Parros, 39 C Travis Green; DET 31 G Joey MacDonald, 24 D Chris Chelios, 29 C Jason Williams
The Anaheim Ducks top the Western Conference, but it may not last long considering their recent struggles. The Detroit Red Wings need to snap out of their sudden funk to take advantage.
The Ducks look to avoid their first five-game losing streak in four years when they face the conference rival Red Wings on Sunday.
Anaheim (28-9-6) leads the West with 62 points, seven ahead of Detroit (25-11-5).
The Ducks, however, have lost four straight games in regulation for the first time since Nov. 13-20, 2005. They haven't lost five in a row since Dec. 26, 2002-Jan. 3, 2003.
With a three-goal lead and Ilya Bryzgalov playing well in net, Anaheim seemed assured of ending its slide against Columbus on Friday night. But the Ducks allowed four goals in the final 10:02 en route to a 4-3 defeat.
"There are certain things we pride ourselves on as far as playing strong defensive hockey, and that went out the window," Anaheim coach Randy Carlyle said.
Ducks leading scorer Teemu Selanne had a goal early in the third period, but missed a chance to force overtime when Columbus goalie Fredrik Norrena blocked his penalty shot with 21 seconds remaining.
"It's embarrassing and that's the only word I can use to describe the whole thing," Selanne said.
Bryzgalov, on the shelf with a groin injury until recently, started his second game in a row and faced 33 shots in the loss. He is 1-2-0 with a 2.02 goals-against average in three career games against the Red Wings.
The Ducks remain plagued by injuries. Anaheim is missing defensemen Chris Pronger (fractured foot) and Francois Beauchemin (lacerated spleen), and forward Todd Marchant (abdominal strain) in addition to goaltender Jean-Sebastien Giguere (groin).
Detroit, meanwhile, has lost consecutive games in regulation for just the second time this season. The Red Wings had a three-game losing streak from Oct. 18-21.
"We haven't been playing as well as we can and we've given up a couple of leads lately," goaltender Chris Osgood said. "That's what happens when you take penalties. They wore us down. We've been short-handed a lot the last two games and we haven't gotten too many power plays. And anytime that happens, you're spending a lot of time in your own end."
The Red Wings didn't convert on two power-play chances in a 4-2 loss at Los Angeles on Saturday night.
Detroit center Pavel Datsyuk missed his third straight game because of a groin injury. His status for Sunday's game is uncertain.
Defenseman Chris Chelios sat out his fifth straight game and third since two employees were stabbed to death at his Detroit sports bar. Chelios is expected to rejoin the team Monday in Denver.
Kris Draper and Mikael Samuelsson scored for the Red Wings, who are four points behind Central Division-leading Nashville at the midway mark in their schedule.
Detroit and Anaheim have split two games this season, with each team winning at home. In their last meeting, Tomas Holmstrom had a goal and an assist to lead the Red Wings to a 2-1 win over the Ducks on Jan. 2.